Question

What is the area ABCD with vertices
A(-4,-6)
B(6, -6)
C(-1, 5)
D(9, 5)

Answer 1

okay. So you can either graph or use the distance formula and you have to find the distance between A and B and B and C then multiply. DO you know how to do that?

Answer 2

whats the formula?

Answer 3

@ab60093

Answer 4

oh. Well, personally its easier to graph but the distance formula is
\[d=\sqrt{(x1-x2)^{2}+(y1-y2)^{2}}\]

Answer 5

so i do that to each one? will it be the final answer?

Answer 6

You would only have to do it to AB and BC and no that wouldn't be the answer.so it would be set up like this for AB
\[d=\sqrt{(-4-6)^{2}+(-6-(-6))^{2}}\]

Answer 7

and BC would be something like this
\[BC=\sqrt{(6-(-1))^{2}+(-6-5)^{2}}\]

Answer 8

for AB its
\[AB=\sqrt{(10)^{2}+(0)^{2}}\]

Answer 9

so the answer would be square root of 100?

Answer 10

for AB

Answer 11

yes. For AB

Answer 12

okay now for CD i do the same like AB?

Answer 13

Not quite. You would do BC not CD. And i wrote the equation up top

Answer 14

so it would be (7)^2+(11)^2?

Answer 15

Correct!

Answer 16

so its \[\sqrt{170}\]

Answer 17

i got 178

Answer 18

its 7x7 which is 49 plus 11x11 which is 121. 121+49=170

Answer 19

oh okay

Answer 20

am i done yet?

Answer 21

not quite. You must now multiply the lengths of AB and BC. so
10 x square root of 170

Answer 22

THAT would be the answer

Answer 23

130.384048104?

Answer 24

yeah. or just \[10\sqrt{170}\]

Answer 25

another way to do this would have been the Pythagorean theorem but that would have been the same amount of work

Answer 26

omg thank you so much!

Answer 27

No problem!

Answer 28

i have one more problem though

Answer 29

okay

Answer 30

what is the area of DEF with vertices
D(-1, -5)
E(4, -5)
F(4, 7)

Answer 31

ooo. Triangle. fun

Answer 32

ahaha

Answer 33

okay. this one is going to be a little bit different to make our lives easier. We are going to use the graphing style. so when you do this you get a right triangle. do you know how to find the area of a right triangle?

Answer 34

A=ab
2?

Answer 35

a=ab/2?

Answer 36

yep. hold on like 2 seconds though

Answer 37

okie

Answer 38

okay. Sorry i was ordering food. ANYWAYS, uhhh the distance between E and F is 12 because...it just is. When you look at a graph the distance is 12, if you want we can do the distance formula to check later.
The distance between D and E is 5. You would now have to set up the formula
\[A=\frac{ d \times e }{ 2 }\]

Answer 39

wait oops

Answer 40

\[A=\frac{ DE \times EF }{ 2 }\]

Answer 41

so input values and solve

Answer 42

okay hold on let me solve this lol

Answer 43

so for D do i put -1 or -5?

Answer 44

@ab60093

Answer 45

oh, lol sorry

Answer 46

its alright

Answer 47

it would be
\[A=\frac{ (5\times 12) }{ 2 }\]

Answer 48

You wouldn't use the coordinates in the equation. You would use the distance between the coordinates

Answer 49

30?